document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=293503>Question 293503</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For each equation, state the x-intercept and y-intercept. Then graph the equation using the intercepts and a third point.\r<BR>\n" );
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document.write( "Helen's Health Foods usually sells 400 cans of ProPac Punch per week when the price is $5 per can.  After experimenting  with prices for some time. Helen has determined that the weekly demand can be found by using the equation d=600-40p, where d is te number of cans and p is the price per can.<BR>\n" );
document.write( "a)Will Helen sell more or less Muscle Punch if she raises her price from $5?<BR>\n" );
document.write( "b)What happens to her sales every time she raises her price by $1?<BR>\n" );
document.write( "c)Graph the equation.<BR>\n" );
document.write( "d)What is the maximum price that she can charge and still sell at least one can?<BR>\n" );
document.write( " Can you please help me with this problem? thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #211864 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=211864\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> d = 600 - 40p<BR>\n" );
document.write( "d is the number of cans<BR>\n" );
document.write( "p is the price per can\r<BR>\n" );
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document.write( "When p = 5, d = 600 - 40*5 = 600 - 200 = 400 cans per week.\r<BR>\n" );
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document.write( "When p = 6, d = 600 - 40*6 = 600 - 240 = 360 cans per week.\r<BR>\n" );
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document.write( "When p = 7, d = 600 - 40*7 = 600 - 280 = 320 cans per week.\r<BR>\n" );
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document.write( "Every dollar increase in the price means 40 less cans sold per week.\r<BR>\n" );
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document.write( "Your questions are:\r<BR>\n" );
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document.write( "a)Will Helen sell more or less Muscle Punch if she raises her price from $5?\r<BR>\n" );
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document.write( "She will sell less punch.\r<BR>\n" );
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document.write( "b)What happens to her sales every time she raises her price by $1?\r<BR>\n" );
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document.write( "She sells 40 less cans per week.\r<BR>\n" );
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document.write( "c)Graph the equation.\r<BR>\n" );
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document.write( "To graph this equation, change d to y and change p to x.<BR>\n" );
document.write( "Your equation becomes y = 600 - 40*x<BR>\n" );
document.write( "Graph of your equation looks like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C20%2C-100%2C900%2C600-40x%2C600%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C20%2C-100%2C900%2C600-40x%2C600%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "d)What is the maximum price that she can charge and still sell at least one can?\r<BR>\n" );
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document.write( "From the graph, it's clear that when she sells at $15.00 per can, she will not sell any cans.\r<BR>\n" );
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document.write( "From the formula, this becomes d = 600 - 40*15 = 600 - 600 = 0\r<BR>\n" );
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document.write( "As long as the price is less than $15.00 per can, she will sell something, even if it's just part of a can.\r<BR>\n" );
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document.write( "Since she can't really sell part of a can, the smallest increment she can sell is 1 can.\r<BR>\n" );
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document.write( "We can figure out what the highest price has to be in order for her to sell 1 can.\r<BR>\n" );
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document.write( "The formula is:\r<BR>\n" );
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document.write( "d = 600 - 40*p\r<BR>\n" );
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document.write( "We set d = 1 to get:\r<BR>\n" );
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document.write( "1 = 600 - 40*p\r<BR>\n" );
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document.write( "We subtract 1 from both sides of this equation and we add 40*p to both sides of this equation to get:\r<BR>\n" );
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document.write( "40*p = 599\r<BR>\n" );
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document.write( "We divide both sides of this equation by 40 to get:\r<BR>\n" );
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document.write( "p = 599/40 = $14.975 per can.\r<BR>\n" );
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document.write( "At that price, she will sell 1 can.\r<BR>\n" );
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document.write( "That's the highest price she can sell each can for and still be able to sell at least 1 can based on the formula.\r<BR>\n" );
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document.write( "Her price must be less than or equal to $14.975 in order for her to sell at least 1 can.\r<BR>\n" );
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document.write( "That's the answer to question d.\r<BR>\n" );
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document.write( "The rest is just additional information.\r<BR>\n" );
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document.write( "Continue reading only if interested.\r<BR>\n" );
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document.write( "It appears that the differential price per can is equal to $15.00 - $14.975 = $.025.\r<BR>\n" );
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document.write( "This means that if she drops the price by another $.025, she should be able to sell exactly 1 more can.\r<BR>\n" );
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document.write( "To see if that works, we put that into the formula.\r<BR>\n" );
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document.write( "The formula is d = 600 - 40*p\r<BR>\n" );
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document.write( "We set p = $14.975 and we get d = 600 - 40*14.975 = 600 - 599 = 1\r<BR>\n" );
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document.write( "We set p = $14.950 and we get d = 600 - 40*14.950 = 600 - 598 = 2\r<BR>\n" );
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document.write( "The increment for selling exactly 1 more or less cans is equal to $.025 per can.\r<BR>\n" );
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document.write( "That makes sense because in the formula d = 600 - 40*p, if we just look at the 40*p part, we see that 40*.025 = 1, 40*.05 = 2, etc.\r<BR>\n" );
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document.write( "Your answer to question d is that the maximum price per can in order for her to sell at least 1 can is $14.975 per can.\r<BR>\n" );
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